Double Dragon for the Game Boy is a pseudo-port of the NES version. It has most of the attacks from that version, but it drops the XP mechanic and changes around stages and enemy placement. Like the original, it's a single player game.
The only attacks missing from this version are the sit-on punch, which allows you to punch grounded enemies into submission, and the High Kick, which is already upgraded to the Roundhouse Kick.
To execute the Back Elbow and Backwards Kick attacks, press Select + A or B, respectively.
Double Dragon is a re-worked port of the NES version that gets rid of the XP system and slightly reworks the stages and enemy layouts. Although you only fight two enemies at once, it has the NES version's complete moveset. The graphics are good and the music is iconic as ever.